Tidal fields in general relativity - d'Alembert's principle and the test rigid rod

Astronomy and Astrophysics – Astronomy

Scientific paper

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Black Holes (Astronomy), Gravitational Fields, Relativistic Particles, Relativity, Tides, Gyroscopes, Riemann Manifold, Spin Dynamics, Tensor Analysis

Scientific paper

To the general relativist, tidal forces are a manifestation of the Reimann tensor; the relativist therefore uses the Reimann tensor to calculate the effects of such forces. In contrast, we show that the introduction of gravitational 'probes' (or 'test rigid rods') and the adoption of a viewpoint closely allied to d'Alembert's principle, give an enormous simplification in cases of interest. No component of the Reimann tensor need be calculated as such. In the corotating orbital case (or Roche problem) the calculation of the relevant distortional field becomes trivial. As a by-product of this investigation, there emerges an illuminating strong field generalization of de Sitter's weak field precession for slowly spinning gyroscopes.

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